The difficulty in escaping Springer/Elsevier is not that researchers are too dumb to organize their own journals/peer review. Quite the opposite, we already do that FOR Springer/Elsevier.
The difficulty is that existing publishers own journals which have gathered significant prestige over decades and sometimes centuries. And hiring boards, swamped and unable to take a closer look, often just look at which journals a prospect has published in. That means if you're not submitting to these prestigious journals, you're crippling yourself. And by submitting to them, you're adding to their prestige, making it a vicious self-feedback loop.
Or if you get the entire editorial board to resign, and start a new journal.
This happened with the board of Topology (http://www.ams.org/notices/200705/comm-toped-web.pdf), who then set up the Journal of Topology. The new journal isn't open access, but it is cheaper. Then the editors of K-theory resigned to set up the Journal of K-theory, which was less than half the price of its predecessor.
So can't you submit some papers to the prestigious journals, and others to the not so prestigious journals?
Out of interest, does prestige really advance society and/or the sciences in any way? Genuine question - if the answer is yes, then how does it do this?
The difficulty is that existing publishers own journals which have gathered significant prestige over decades and sometimes centuries. And hiring boards, swamped and unable to take a closer look, often just look at which journals a prospect has published in. That means if you're not submitting to these prestigious journals, you're crippling yourself. And by submitting to them, you're adding to their prestige, making it a vicious self-feedback loop.